Biomedical Engineering Reference
In-Depth Information
specied). Pan 36 considered the problem of extending Akaike's derivation
of AIC to GEE models. Pan's procedure works best with a working in-
dependent correlation matrix, so we use this formulation. With working
independence, the GEE model t can be seen as a maximum pseudo quasi-
likelihood t. To take into account the within-subject correlation, Pan 36
sets the degrees of freedom for a GEE estimate
b
with working indepen-
dent correction matrix to be
b
b
df P = tr(
V);
b
where
is the observed Fisher information matrix for the logarithm of
pseudo quasi-likelihood denoted by QL(), i.e.,
b
b
)=@@ T ,
=@ 2 QL(
b
b
and
using robust sandwich for-
mula. Pan 36 thus suggests selecting signicant variables by minimizing the
following the quasi-AIC (QIC)
V is the estimated covariance matrix of
b
QIC =2QL(
) + 2df P :
(4.4)
See [36] for heuristic derivation of these formulas. This QIC is similar to
Takeuchi's information criterion, a more general form of Akaike's infor-
mation criterion in the classical case; it is also closely related to earlier
adjustments to AIC for overdispersion (see [6, pp. 65-69]). If the responses
are independent and the model is adequate, then QIC is equivalent to AIC.
However, QIC's reliance on working independence may make it less eective
if within-subject correlation is high.
Ad hoc generalization of the BIC is possible along the same lines, al-
though the ambiguity of the sample size becomes a diculty (see [38]
and [20]). Naive possibilities include2QL(
b
b
) + log(n)df and2QL(
) +
log(N)df, but more research is needed.
We conclude this section with a remark. Although several authors have
made eorts in developing variable selection for GEE model t, it is not
clear which measure of model t is the best or which denition of degrees
of freedom will perform best. Further research to provide both theoreti-
cal insights and empirical justication for extending traditional variable
selection procedures to longitudinal data are clearly needed. Some other
practical remarks on GEE model selection are found in [3].
4.2. Penalized GEE
In this section, we extend the non-concave penalized likelihood
approach 45;15 to GEE model tting. We combine selection and esti-
mation by solving the following penalized generalized estimating
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